Interaction energies of large clusters from many-body expansion

In the canonical supermolecular approach, calculations of interaction energies for molecular clusters involve a calculation of the whole cluster, which becomes expensive as the cluster size increases. We propose a novel approach to this task by demonstrating that interaction energies of such clusters can be constructed from those of small subclusters with a much lower computational cost by applying progressively lower-level methods for subsequent terms in the many-body expansion. The efficiency of such "stratified approximation" many-body approach (SAMBA) is due to the rapid convergence of the many-body expansion for typical molecular clusters. The method has been applied to water clusters (H(2)O)(n), n = 6, 16, 24. For the hexamer, the best results that can be obtained with current computational resources in the canonical supermolecular method were reproduced to within about one tenth of the uncertainty of the canonical approach while using 24 times less computer time in the many-body expansion calculations. For (H(2)O)(24), SAMBA is particularly beneficial and we report interaction energies with accuracy that is currently impossible to obtain with the canonical supermolecular approach. Moreover, our results were computed using two orders of magnitude smaller computer resources than used in the previous best calculations for this system. We also show that the basis-set superposition errors should be removed in calculations for large clusters.     

Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy

Using the variational technique, eigensolutions of the radial Herman-Asgharian equation accounting for non-adiabatic terms are determined within the experimental accuracy of the high-resolution spectroscopy. This method, which is independent of the algebraic and numerical approaches currently used in the literature for a "direct-potential-fit" of diatomic rovibrational spectra, is shown to be useful for validation of available calculations and for resolving some controversial issues. Comparative discussions are reported in this paper for a dozen diatomic molecules.     

Calculation of bound-state energies from a variational functional method

A variational functional method is improved and generalized in order to obtain approximate bound-state energies of a wide variety of quantum-mechanical systems. Calculations on the discrete spectrum of the hydrogen atom in a magnetic field and the bounded harmonic oscillator show that the procedure is very promising.     

Excited-state energies from many-body perturbation theory with the excitation-adapted one-particle potential

Calculation of excited-state energies by many-body perturbation theory is discussed. A Hartree-Fock-type potential suitable for a given excited-state configuration is introduced. Advantages which follow from the excitation-adapted one-particle potential are examined. The theory resembles that for external perturbation effects and amounts to removing or minimizing the contribution of non-diagonal one-particle terms.     

Communication: variational many-body expansion: accounting for exchange repulsion, charge delocalization, and dispersion in the fragment-based explicit polarization method

A fragment-based variational many-body (VMB) expansion method is described to directly account for exchange repulsion, charge delocalization (charge transfer) and dispersion interactions in the explicit polarization (X-Pol) method. The present VMB/X-Pol approach differs from other fragment molecular orbital (FMO) techniques in two major aspects. First, the wave function for the monomeric system is variationally optimized using standard X-Pol method, as opposed to the iterative update procedure adopted in FMO. Second, the mutual polarizations in the dimeric terms are also variationally determined, whereas single-point energy calculations of the individual dimers embedded in a static monomer field are used in FMO. The second-order (two-body) VMB (VMB2) expansion method is illustrated on a series of water hexamer complexes and one decamer cluster, making use of Hartree-Fock theory, MP2, and the PBE1 and M06 density functionals to represent the monomer and dimer fragments. The computed binding energies are within 2 kcal/mol of the corresponding results from fully delocalized calculations. Energy decomposition analyses reveal specific dimeric contributions to exchange repulsion, charge delocalization, and dispersion. Since the wave functions for one-body and all two-body terms are variationally optimized in VMB2 and X-Pol, it is straightforward to obtain analytic gradient without the additional coupled-perturbed Hartree-Fock step. Thus, the method can be useful for molecular dynamics simulations.     

New double many-body expansion potential energy surface for ground-state HCN from a multiproperty fit to accurate ab initio energies and rovibrational calculations

An accurate single-sheeted double many-body expansion potential energy surface has been obtained for the ground electronic state of the hydrogen cyanide molecule via a multiproperty fit to ab initio energies and rovibrational data. This includes 106 rovibrational levels and 2313 discrete points, which are fit with a rmsd of 4 cm(-1) and 2.42 kcal mol(-1), respectively, and seven zero first-derivatives that are reproduced at three stationary points. Since the potential also describes accurately the appropriate asymptotic limits at the various dissociation channels, it is commended both for the simulation of rovibrational spectra and reaction dynamics.     

Theoretical modeling of ionization energies of argon clusters: nuclear delocalization effects

Temperature dependence of vertical ionization energies is modeled for small argon clusters (N ≤ 13) using classical parallel-tempering Monte Carlo methods and extended interaction models based on the diatomics-in-molecules approach. Quantum effects at the zero temperature are also discussed in terms of zero-point nuclear vibrations, either at the harmonic approximation level or at the fully anharmonic level using the diffusion Monte Carlo calculations. Both approaches lead to a considerable improvement of the theoretical predictions of argon clusters ionization energies and represent a realistic way of modeling of ionization energies for weakly bound and floppy complexes in general. A thorough comparison with a recent electron-impact experiment [O. Echt et al., J. Chem. Phys. 123, 084313 (2005)] is presented and a novel interpretation of the experimental data is proposed.     

Improved perturbative treatment of electronic energies from a minimal-norm approach to many-body perturbation theory

We propose a zeroth-order Hamiltonian for many-body perturbation theory based on the unitary decomposition of the two-particle reduced Hamiltonian. For the zeroth-order Hamiltonian constrained to be diagonal in the Hartree-Fock basis set, the two-particle reduced perturbation matrix is chosen to have a minimal Frobenius norm. When compared with the M?ller-Plesset partitioning, the method yields more accurate second-order energies.     

Ionization energies of argon clusters: a combined experimental and theoretical study

We have measured appearance energies of Ar(n)+, n相似文献   

On a new partitioning of the Hamiltonian in many-body calculation of pair-correlation energies in closed-shell systems

We introduce here a new partitioning of the Hamiltonian in calculating pair-correlation energies using many-body perturbation theory, by which we are able to eliminate the off-diagonal particle–hole (p–h) ladders exactly to all orders in the perturbation expansion. In this formulation, the particle states turn out to be different for each distinct pair of hole states in the correlation energy calculation. We have also included the contributions of the diagonal particle–particle (p–p) and hole–hole ladders exactly to all orders. The effect of the off-diagonal p–p ladders has been estimated for each pair by computing the third-, foruth- and fifth-order energies. For highly symmetric systems the present partitioning yields in general symmetry-broken orbitals. Here one may use an average kind of partitioning for all the partners of the degenerate sets, which restores the symmetry and at the same time ensures cancellation of the p–h ladders exactly at the lowest order and approximately at the higher orders. Results are presented for a selection of 6π-electron conjugated systems. The correlation energy for each pair is in excellent agreement with that obtained from a partial CI calculation involving all double excitations from this pair. The advantages of implementing the present scheme in larger systems has been discussed.     

A realistic double many-body expansion potential energy surface for SO2(X1A') from a multiproperty fit to accurate ab initio energies and vibrational levels

A single-valued double many-body expansion potential energy surface (DMBE I) recently obtained for the ground electronic state of the sulfur dioxide molecule by fitting correlated ab initio energies suitably corrected by scaling the dynamical correlation energy is now refined by fitting simultaneously available spectroscopic levels up to 6886 cm(-1) above the minimum. The topographical features of the novel potential energy surface (DMBE II) are examined in detail, and the method is emphasized as a robust route to fit together state-of-the-art theoretical calculations and spectroscopic measurements using a single fully dimensional potential form.     

A generalized many-body expansion and a unified view of fragment-based methods in electronic structure theory

Fragment-based quantum chemistry methods are a promising route towards massively parallel electronic structure calculations in large systems. Unfortunately, the literature on this topic consists of a bewildering array of different methods, with no clear guiding principles to choose amongst them. Here, we introduce a conceptual framework that unifies many of these ostensibly disparate approaches. The common framework is based upon an approximate supersystem energy formula for a collection of intersecting (i.e., overlapping) fragments. This formula generalizes the traditional many-body expansion to cases where the "bodies" (fragments) share some nuclei in common, and reduces to the traditional many-body expansion for non-overlapping fragments. We illustrate how numerous fragment-based methods fit within this framework. Preliminary applications to molecular and ionic clusters suggest that two-body methods in which dimers are constructed from intersecting fragments may be a route to achieve very high accuracy in fragment-based calculations.     

Nonadditive effects in the mixed trimers of HCl and methanethiol

Ab initio and density functional theory calculations with aug-cc-pVDZ and aug-cc-pVTZ basis sets have been performed on the HCl-CH3SH dimer and HCl-(CH3SH)2 and (HCl)2-CH3SH trimers. Structures, energetics, and infrared frequencies are calculated. The results are discussed in terms of the cooperativity effect which is a characteristic of H-bonded systems and compared to oxygen-containing analogs of the same trimers, HCl-(CH3OH)2 and (HCl)2-CH3OH, which have been published recently.     

Estimating relative free energies from a single ensemble: Hydration free energies

The ability to determine the free energy of solvation for a number of small organic molecules with varying sizes and properties from the coordinate trajectory of a single simulation of a given reference state was investigated. The relative free energies were estimated from a single step perturbation using the perturbation formula. The reference state consisted of a cavity surrounded by solvent. To enhance sampling a soft-core interaction was used for the cavity. The effect of the size of the cavity, the effective core height, and the length of simulation on the ability to reproduce results obtained from thermodynamic integration calculations was considered. The results using a single step perturbation from an appropriately chosen initial state were comparable to results from thermodynamic integration calculations for a wide range of compounds. Using a large number of compounds the computational efficiency was potentially increased by 2–3 orders of magnitude over traditional free energy approaches. Factors determining the efficiency of the approach are discussed. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1604–1617, 1999     

Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method

The variational two-electron reduced-density-matrix (2-RDM) method allows for the computation of accurate ground-state energies and 2-RDMs of atoms and molecules without the explicit construction of an N-electron wave function. While previous work on variational 2-RDM theory has focused on calculating full configuration-interaction energies, this work presents the first application toward approximating multiconfiguration self-consistent-field (MCSCF) energies via low-rank restrictions on the 1- and 2-RDMs. The 2-RDM method with two- or three-particle N-representability conditions reduces the exponential active-space scaling of MCSCF methods to a polynomial scaling. Because the first-order algorithm [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] represents each form of the 1- and 2-RDMs by a matrix factorization, the RDMs are readily defined to have a low rank rather than a full rank by setting the matrix factors to be rectangular rather than square. Results for the potential energy surfaces of hydrogen fluoride, water, and the nitrogen molecule show that the low-rank 2-RDM method yields accurate approximations to the MCSCF energies. We also compute the energies along the symmetric stretch of a 20-atom hydrogen chain where traditional MCSCF calculations, requiring more than 17x10(9) determinants in the active space, could not be performed.     

Thermal expansion effects in a silo

We consider a vertical container filled with granular material and exposed to temperature cycles which induce changes in the pressure distribution. Our starting point is an elastic model for the grains leading to classical Janssen behaviour in isothermal conditions. We assume complete mobilisation of the wall frictions. The dynamics superposes static friction plus a viscous friction. After a T jump favouring an expansion, we predict that the resulting overpressures are relaxed only in a region (of size comparable to the Janssen screening length λ) near the top. When T returns to the initial value, we expect decohesion in a certain layer near the top (for rapid cooling). For slow cooling, we expect a smooth return to the original Janssen state. We also discuss a different, but related, effect: instead of changing the temperature, we switch off the gravity effects (on a small column) by suddenly rotating the column from vertical to horizontal. Here, a rarefaction wave should invade the whole column.     

Relativistic, quantum electrodynamic and many-body effects in the water molecule

Ab initio calculations are reported of the electronic structure of the water molecule, based on the Dirac theory of the electron using correlation consistent basis sets. We calculate electron correlation corrections by second-order many-body perturbation theory, NMR shielding constants in the four-component relativistic interaction Hamiltonian formulation of QED, and report the first calculation of the electronic structure of a molecular system in which the Breit interaction is included both perturbatively and variationally in the calculation of the total energy.